OFFSET
1,2
FORMULA
EXAMPLE
G.f.: A(x) = x + 3*x^3 + 27*x^5 + 339*x^7 + 5067*x^9 +...
A(x)^3 = x^3 + 9*x^5 + 108*x^7 + 1530*x^9 + 24219*x^11 +...
A(x) = G(G(G(x))) where
G(x) = x + x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 +...
A(x) = F(x) + x^2*H(x)^3 where
F(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 +...
H(x) = x + 4*x^3 + 42*x^5 + 594*x^7 + 9827*x^9 +...
H(x)^3 = x^3 + 12*x^5 + 174*x^7 + 2854*x^9 + 51045*x^11 +...
PROG
(PARI) {a(n)=local(G=x+O(x^(2*n+1))); for(i=0, n, G=serreverse(x-G^3)); polcoeff(subst(G, x, subst(G, x, G)), 2*n-1)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 21 2009
STATUS
approved